R Notebook

library(tidyverse)
library(plotly)

load("wireless.rda")

plot(x=wireless$x, y=wireless$y)
points(x=AP$x,y=AP$y, col="red", cex=1)

# exploring relationship between distance and signal strength
# without the loss of generality, use X
ap1 = as.numeric(AP[1,])
distances = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - ap1)^2))})
par(mfrow=c(2,2))
plot(y=distances[distances > cutoff]^2, x=-wireless$S1[distances > cutoff])
plot(x=log(-wireless$S1[distances > cutoff]), y=2*log(distances[distances > cutoff]))

plot(y=distances, x=-wireless$S1)
plot(x=log(-wireless$S1[distances > cutoff]), y=log(distances[distances > cutoff]))

mod = lm(wireless$S2~log(distances2))
summary(mod)

Call:
lm(formula = wireless$S2 ~ log(distances2))

Residuals:
     Min       1Q   Median       3Q      Max 
-17.6911  -3.9331  -0.2897   3.8617  17.3204 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)       4.2900     2.5687    1.67   0.0961 .  
log(distances2) -18.1938     0.5488  -33.15   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.86 on 252 degrees of freedom
Multiple R-squared:  0.8135,    Adjusted R-squared:  0.8127 
F-statistic:  1099 on 1 and 252 DF,  p-value: < 2.2e-16

TODO: try to do that for S2, S3… as well

# exploring relationship between distance and signal strength
# without the loss of generality, use X
ap2 = as.numeric(AP[2,])
distances2 = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - ap2)^2))})
par(mfrow=c(2,2))
plot(y=(distances2[distances2 < cutoff])^2, x=-wireless$S2[distances2 < cutoff])
plot(x=log(-wireless$S2[distances2 < cutoff]), y=2*log(distances2[distances2 < cutoff]))

plot(y=distances2[distances2 < cutoff], x=-wireless$S2[distances2 < cutoff])
plot(x=log(-wireless$S2[distances2 < cutoff]), y=log(distances2[distances2 < cutoff]))

plot(x=(distances2)[distances2 < cutoff], y=-wireless$S2[distances2 < cutoff])

#for distance above 100, the linear relationship between signal and distance breaks
#lots of points have -92 the worse signal ever 

mod2 = lm(wireless$S2[distances2 < cutoff]~distances2[distances2 < cutoff])
mod1 = lm(wireless$S1[distances < cutoff]~distances[distances < cutoff])
dx = (wireless[knn_predictions[223],4] -wireless[223,4])/mod$coefficients[2] * 
  (wireless[223,4]-mod$coefficients[1])/mod$coefficients[2] /
  (wireless[knn_predictions[223],1]-AP$x[2])
dy = (wireless[knn_predictions[223],4] -wireless[223,4])/mod$coefficients[2] * 
  (wireless[223,4]-mod$coefficients[1])/mod$coefficients[2] /
  (wireless[knn_predictions[223],2]-AP$y[2])

1/test2

             x          y
[1,] -1.266179 -26.674175
[2,]  3.147891  -5.036626
[3,]  4.904649   2.239919
[4,] -1.533693   4.114786
[5,] -1.273203   8.885615

k = mod2$coefficients[2]
b = mod2$coefficients[1]
signals = wireless_feature[224,]
test = t(apply(AP, 1, function(x) {as.numeric(wireless[224,1:2]) - x}))
test2 = apply(test, 2, function(x) as.numeric(k^2/(signals - b)) * x)
df_mod = lm(as.numeric(wireless_feature[223,] - wireless_feature[224,])~0 + 
                         test2[,1] + test2[,2])
summary(df_mod)

Call:
lm(formula = as.numeric(wireless_feature[223, ] - wireless_feature[224, 
    ]) ~ 0 + test2[, 1] + test2[, 2])

Residuals:
      1       2       3       4       5 
 0.2427  5.0153  1.8677 -0.5638  2.7374 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)
test2[, 1]   -2.071      2.681  -0.773    0.496
test2[, 2]   -3.237      6.455  -0.502    0.651

Residual standard error: 3.489 on 3 degrees of freedom
Multiple R-squared:  0.1886,    Adjusted R-squared:  -0.3523 
F-statistic: 0.3487 on 2 and 3 DF,  p-value: 0.7308

##exploring using differentials 
##
sample_index = sample(1:nrow(wireless), 1)
sample_point = wireless[sample_index,]
sample_diff = data.frame(t(apply(wireless[-sample_index,], 1, function(x) x - as.numeric(wireless[sample_index,]))))
sample_diff_y = sample_diff[sample_diff$y == 0,]
mod = lm(x~.-y, data=sample_diff_y)
summary(mod)

Call:
lm(formula = x ~ . - y, data = sample_diff_y)

Residuals:
     Min       1Q   Median       3Q      Max 
-25.7877  -7.6092  -0.1254   9.2944  19.8359 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.6899     8.1992   0.084   0.9336    
S1           -1.3331     0.6897  -1.933   0.0638 .  
S2            3.7611     0.4953   7.593 3.62e-08 ***
S3           -1.5752     1.0351  -1.522   0.1397    
S4           -0.7039     0.9135  -0.771   0.4477    
S5            0.7194     0.4555   1.579   0.1259    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 11.43 on 27 degrees of freedom
Multiple R-squared:  0.9664,    Adjusted R-squared:  0.9602 
F-statistic: 155.3 on 5 and 27 DF,  p-value: < 2.2e-16

avg_error

[1] 17.20438

plot(wireless$x, wireless$y)
points(basic_x$fitted.values, basic_y$fitted.values, col="red")

segments(wireless$x, wireless$y, basic_x$fitted.values, basic_y$fitted.values, col="blue")

n = nrow(wireless)
#train_percent = 0.6
#sample_indices = sample(1:nrow(wireless), train_percent*n)
knn_predictions = numeric(n)
wireless_feature = wireless[,3:7]
pwdistances = as.matrix(dist(wireless_feature))
for (i in 1:n) {
  knn_predictions[i] = (1:n)[-i][which.min(as.matrix(pdist::pdist(wireless_feature[i,], wireless_feature[-i,])))]
}
knn_predictions

  [1]  24  23   6 156   6 181 101  37  36  11  10  10  14 182  14  86  86  16  18  24  19 102   2  25  24  27  26  30  31  28
 [31]  32  31  31  33 186  37  36  49  43 253  49  46  39 253  49  42  79  83  41  51  50  80  65  57  56  54  54  59  60  59
 [61]  62  61  64  63  53  93  66  63  46  71  70  83  74  73  74  77  81  77  76  52  77 204  72  95 106 107 147 108 119 100
 [91]  74  65  66 103  84 106 107 108  89  90 239  22  94 240  95  85  86  98 119 120 127 144  33  29 161 135  97  98  89 110
[121] 175 127 144 149 153 133 166 130 160 128 154 133 126 135 134 135 138 137 138 165 165 131 123 123 147 147 146 150 124 148
[151] 152 151 125 131 153 157 156 159 160 129 129 163 162 135 140 127 146 177 173 166 176 168 169 191 179 191 168 188 175 191
[181]   6  10  86  27  99  35 195 178 234 179 174 178 198 221 187 212 249 241 219 204 238 233 233 236 222 207 206 206 211 211
[211] 209 213 212 196 217 222 215 217 217 247 194 216 224 223 226 225 229 241 227 229 244 244 203 235 234 204 213 201 101 104
[241] 228 247  44 232 249 250 242 252 197 246 254 248  40 251

knn_x = wireless$x[knn_predictions]
knn_y = wireless$y[knn_predictions]
knn_avg_error = mean(sqrt((wireless$x - knn_x)^2 + (wireless$y - knn_y)^2))
knn_avg_error

[1] 10.97828

par(mfrow=c(1,2))
plot(density(sqrt((wireless$x - knn_x)^2 + (wireless$y - knn_y)^2)),
     main = "knn performance")
plot(density(sqrt((wireless$x - basic_x$fitted.values)^2 + (wireless$y - basic_y$fitted.values)^2)),
     main = "regression performance")

knn_errors = sqrt((wireless$x - knn_x)^2 + (wireless$y - knn_y)^2)

plot(wireless$x, wireless$y)
points(knn_x, knn_y, col="red")

segments(wireless$x, wireless$y, knn_x, knn_y, col="blue")

num_iter = 1000
coef_x = matrix(-1, nrow=num_iter, ncol=5)
coef_y = matrix(-1, nrow=num_iter, ncol=5)
singularities = 0
for (i in 1:num_iter) {
  Error = TRUE
  while (Error) {
    tryCatch(
      {
        sample_indices = sample(1:n,5)
        temp_A = wireless_feature[sample_indices,]
        temp_bx = wireless$x[sample_indices]
        temp_by = wireless$y[sample_indices]
        temp_x = solve(temp_A, temp_bx)
        temp_y = solve(temp_A, temp_by)
      Error = FALSE
      },
      error=function(cond) {
      }
    )}
  coef_x[i,] = temp_x 
  coef_y[i,] = temp_y 
}
dx = c(
  mean(coef_x[,1][abs(coef_x[,1]) < 20]),
  mean(coef_x[,2][abs(coef_x[,2]) < 20]),
  mean(coef_x[,2][abs(coef_x[,3]) < 20]),
  mean(coef_x[,2][abs(coef_x[,4]) < 20]),
  mean(coef_x[,2][abs(coef_x[,5]) < 20])
)
dy = c(
  mean(coef_y[,1][abs(coef_y[,1]) < 20]),
  mean(coef_y[,2][abs(coef_y[,2]) < 20]),
  mean(coef_y[,2][abs(coef_y[,3]) < 20]),
  mean(coef_y[,2][abs(coef_y[,4]) < 20]),
  mean(coef_y[,2][abs(coef_y[,5]) < 20])
)

df_avg_error

[1] 13.66296

set.seed(12345)
sample_indices = sample(1:254, 50)
plot(wireless$x[sample_indices], wireless$y[sample_indices], ylim=c(0, 145), xlim=c(10, 235))
points((knn_x-df_x)[sample_indices], (knn_y-df_y)[sample_indices], col="red")

points(knn_x[sample_indices], knn_y[sample_indices], col="yellow")
segments(wireless$x[sample_indices], wireless$y[sample_indices], knn_x[sample_indices], knn_y[sample_indices], col="blue")

segments(knn_x[sample_indices], knn_y[sample_indices], (knn_x-df_x)[sample_indices], (knn_y-df_y)[sample_indices], col="green")

#segments(wireless$x, wireless$y, knn_x+df_x, knn_y+ df_y, col="green")

p = plot_ly(wireless, x=~x, y=~y, name = "receivers", type="scatter", 
            mode="markers", text=paste(1:254, "<br>", hover_text)) %>% 
  add_trace(x=AP$x, y=AP$y, name = "wifi post", mode="markers", text=rownames(AP))
p

kclusters = kmeans(wireless[,3:7], 5)
#kclusters$cluster

ggplot(data=wireless) +
  geom_point(aes(x=x,y=y), colour=kclusters$cluster) 

ggplot(data=wireless) +
  geom_point(aes(x=x,y=y)) +
  scale_fill_manual(kclusters$cluster)

cutoff = 68
# seems like 70 is a good cut off lets check how many points have more than 70
wireless_strong = wireless %>%
  mutate(S1 = S1 > -cutoff) %>% 
  mutate(S2 = S2 > -cutoff) %>% 
  mutate(S3 = S3 > -cutoff) %>% 
  mutate(S4 = S4 > -cutoff) %>% 
  mutate(S5 = S5 > -cutoff) 

# seems like 70 is not a good cutoff as we think
table(apply(wireless_strong[,3:7], 1, sum))

bad_locations = wireless_strong[as.numeric(apply(wireless_strong[,3:7], 1, sum)) < 2,]

plot(x=bad_locations$x, y=bad_locations$y, ylim=c(0,150), xlim=c(0,230))
points(x=AP$x,y=AP$y, col="red", cex=5)

View(data.frame(table(wireless$y)))